A support vector machine algorithm to classify lithofacies and model permeability in heterogeneous reservoirs

Porosity, permeability, and fluid saturation distributions are critical for reservoir characterization, reserves estimation, and production forecasting. Classification of well-log responses into separate electrofacies that can be used to generate local permeability models gives means to predict the spatial distribution of permeability in heterogeneous reservoirs. Recently, support vector machines (SVMs) based on the statistical learning theory have been proposed as a new intelligence technique for both regression and classification tasks. The formulation of support vector machines embodies the structural risk minimization (SRM) principle which has been shown to be superior to the traditional empirical risk minimization (ERM) principle employed by neural networks. SRM minimizes an upper bound on expected risk as opposed to ERM that minimizes the error on the training data. It is this difference which equips SVM with a greater ability to generalize to new wells. Here, a nonlinear SVM technique is applied in a highly heterogeneous sandstone reservoir to classify electrofacies and predict permeability distributions. The SVM classifier is compared to discriminant analysis and probabilistic neural networks. SVM predictions of the permeability are compared to that of a back-propagation and general regression neural networks. Statistical error analysis shows that the SVM method yields comparable or superior classification of the lithology and estimates of the permeability than the neural network methods. A comparison of log-based and core-based clustering reveals that permeability prediction based on core-based clustering were slightly better than that of the log-based clustering.